Republican presidential candidate Ben Carson said Sunday Muslims were unfit to be president of the United States, arguing that the principles of Islam are inconsistent with American values.

"I would not advocate that we put a Muslim in charge of this nation. I absolutely would not agree with that," Carson, a devout Christian, told NBC's Meet the Press.

He said a president's faith should matter to voters and he described the Islamic faith as inconsistent with the Constitution, although he did not specify in what way Islam ran counter to constitutional principles.

Campaign event comments

Carson's comments came amid lingering fallout over Republican Donald Trump's refusal last week to take issue with a man during a New Hampshire campaign event who wrongly called President Barack Obama a Muslim and said Muslims are "a problem in this country."

Trump and Ohio Governor John Kasich, a rival Republican contender, also appeared in separate appearances on the NBC news show.

Kasich was asked whether he would have a problem with a Muslim in the White House.

"The answer is, at the end of the day, you've got to go through the rigors, and people will look at everything," he said. "But, for me, the most important thing about being president is you have leadership skills, you know what you're doing and you can help fix this country and raise this country. Those are the qualifications that matter to me."

Asked whether a Muslim could be elected, Trump said, "Some people have said it already happened, frankly."

When Carson was asked if he believed Obama is a Christian, he said, “I believe that he is. I have no reason to doubt what he says."

Drawing a distinction

In multiple interviews Sunday, Trump tried to draw a distinction between all American-Muslims and extremist Muslims in the U.S. and elsewhere.

"I have friends that are Muslims they're great people, amazing people," Trump said on CNN's State of the Union.

"You have extremists Muslims that are in a class by themselves," Trump added. "It's a problem in this country it's a problem throughout this world. ...You do have a problem with radical Muslims."

Trump has been a vocal skeptic of Obama's birthplace and faith. Obama is Christian.

After the comments made at the Thursday night rally, New Jersey Gov. Chris Christie and Democratic front-runner Hillary Clinton quickly condemned Trump for failing to correct the town hall participant, while most other 2016 contenders remained silent.

Trump said later that he was not "morally obligated to defend the president" against every negative or controversial comment.

Carson also made a distinction when it came to electing Muslims to Congress, calling it a "different story" from the presidency that "depends on who that Muslim is and what their policies are, just as it depends on what anybody else says."

Meanwhile, Carson gave up some ground in a CNN/ORC poll released Sunday, slipping to third place from second with 14 percent of support.

The CNN/ORC poll showed Trump continues to lead the Republican contest with the support of 24 percent of registered voters, down from 32 percent in a previous poll. Former Hewlett-Packard chief executive Carly Fiorina surged into second place with 15 percent support.

"The only poll that matters is the big one. You know that one. It's going to be the election," Trump told CNN's State of the Union in a telephone interview, saying he was surprised by the results.

Fiorina, meanwhile, gained after a strong debate performance in which she icily skewered the brash real estate mogul for disparaging her looks in comments reported by Rolling Stone magazine.

"I think women all over this country heard very clearly what Mr. Trump said," Fiorina said in Wednesday night's debate.

Sixteen Republicans are seeking the party's nomination for the U.S. presidential election in November 2016.